Replace Nginx’s plain default error pages with your own, while keeping the right HTTP status code.

server {
    listen 80;
    server_name example.com;
    root /var/www/example.com;

    # Map status codes to your pages.
    error_page 404              /404.html;
    error_page 500 502 503 504  /50x.html;

    location = /404.html {
        internal;
    }

    location = /50x.html {
        internal;
    }
}

Details:

error_page 404 /404.html; tells Nginx to serve /404.html when a 404 occurs. The browser still receives a 404 status (not 200), which is what crawlers and monitoring expect.
internal; makes /404.html reachable only via an internal redirect (the error handler) — visiting https://example.com/404.html directly returns 404. Without it the page is publicly fetchable.
The error page files live under your root like any static file. Keep them self-contained (inline CSS, no broken asset links) so they render even when the rest of the site is down.

Show your own page for upstream errors too (when proxying):

    location / {
        proxy_pass http://127.0.0.1:3000;
        proxy_intercept_errors on;     # let Nginx replace upstream 5xx with your page
        error_page 502 503 504 /50x.html;
    }

Without proxy_intercept_errors on;, the backend’s own error body is passed through unchanged.

sudo nginx -t && sudo nginx -s reload

Custom 404 and 50x error pages